On the Deterministic-Code Capacity of the Two-User Discrete Memoryless Arbitrarily Varying General Broadcast Channel With Degraded Message Sets

An inner bound on the deterministic-code capacity region of the two-user discrete memoryless arbitrarily varying general broadcast channel (AVGBC) was characterized by Jahn, assuming that the common message capacity is nonzero; however, he did not indicate how one could decide whether the latter capacity is positive. Csiszaacuter and Narayan´s result for the single-user arbitrarily varying channel (AVC) establishes the missing part in Jahn´s characterization. Nevertheless, being based on Ahlswede´s elimination technique, Jahn´s characterization is not applicable for symmetrizable channels under state constraint. Here, the various notions of symmetrizability for the two-user broadcast AVC are defined. Sufficient non-symmetrizability condition that renders the common message capacity of the AVGBC positive is identified using an approach different from Jahn´s. The decoding rules we use establish an achievable region under state and input constraints for the family of degraded message sets codes over the AVGBC